仿照N.C.Hopkins文章[3]中的幂零定义,给出一种与N.C.Hopkins及Noriaki Kamiya的定义方法均不相同的定义方法(最后证明,事实上这种定义的方式在本质上等价于Noriak Kamiya的定义方法[2]).更重要的是,在Noriaki Kamiya的定理3的证明[2]过程中存在着明显的不完善之处,这里作者利用新的方法定义了一种完善而且简洁的证明.
Mimicking Hopkins's definition of nilpotence[3],the author gives a different method of definition of nilpotence which is equivalent to that of Kamiya[2].What's more,the proof of Kamiya's Theorem 3 is incomplete;here the author gives a complete precise proof.
[1] MEYBERG K. Lecture on algebras and triple systems [M]. Charlottesville:University of Virginia 1972.
[2] NORIAKI KAMIYA. The nil radical for Lie or anti-Lie triple systems [J]. Journal of Algebra 1993, 158.
[3] HOPKINS N C. Nilpotent ideals in Lie and Anti-Lie triple systems [J]. Journal of Algebra 1995, 178.
[4] Humphreys J E. Introduction to Lie algebras and representation theory [M]. Heidelberg:Springer-Verlag 1972.
[5] FAULKNER J R, FERRAR J C. Simple anti-Jordan pairs [J]. Communications in Algebra 1980, 8.
[6] LISTER W G. A structure theory of Lie triple systems [J]. Transactions of the American Mathematical Society 1952, 72.
[7] Meng·D·J. Introduction to complex semisimple Lie algebra [M]. 北京:北京大学出版社 1998.
[8] KACV G. Lie superalebra [J]. Advances in Mathematics 1977, 26.